Problem: Reduce to lowest terms: $ \dfrac{2}{5} \div \dfrac{8}{5} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{5}$ is $ \dfrac{5}{8}$ Therefore: $ \dfrac{2}{5} \div \dfrac{8}{5} = \dfrac{2}{5} \times \dfrac{5}{8} $ $ \phantom{ \dfrac{2}{5} \times \dfrac{5}{8}} = \dfrac{2 \times 5}{5 \times 8} $ $ \phantom{ \dfrac{2}{5} \times \dfrac{5}{8}} = \dfrac{10}{40} $ The numerator and denominator have a common divisor of $10$, so we can simplify: $ \dfrac{10}{40} = \dfrac{10 \div 10}{40 \div 10} = \dfrac{1}{4} $